Cost-Volume-Profit
Relationships
EMBA 5403 Fall 2010
Cost Estimation 1
Constant
Std Err of Y Est
R squared
No. of Observations
Degrees of Freedom
X Coefficient(s)
Std Err of Coef.
Fall 2010
EMBA 5403
250
299.304749934466
0.944300518134715
5
3
6.75
0.9464847243
2/109
Estimation (continued)
The results gives rise to the following equation:
Utility Costs = £250 + (£6.75 x # of units produced)
R2 = .944, or 94.4 percent of the variation in setup costs is
explained by the number of setup hours variable.
Fall 2010
EMBA 5403
3/109
Estimation (continued)
Given:
*T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale
test and 3 degrees of freedom)
*Standard error of estimate for this sample at the 95% confidence level
is 598.6
The confidence interval for 300 units is:
TC = £250 + 6.75 (300) + (3.182 x £598.6)
= £2275 + £1911
Fall 2010
EMBA 5403
4/109
Cost Estimation Example 2
 In each month, Exclusive Billiards produces between 4 to
10 pool tables. The plant operates on 40-hr shift to
produce up to seven tables. Producing more than seven
tables requires the craftsmen to work overtime. Overtime
work is paid at a higher hourly wage. The plant can add
overtime hours and produce up to 10 tables per month.
The following table contains the total cost of producing
between 4 and 10 pool tables.
Required: a. compute average cost per pool table for 4 to 10 tables
 Estimate fixed costs per month.
Pool Tables Total Cost
4
62800
5
66000
6
69200
7
72400
8
75800
9
79200
10
82600
Fall 2010
EMBA 5403
5/109
Cost-Volume-Profit Analysis

Examines the behavior of total revenues, total costs, and
operating income as changes occur in the output level, selling
price, variable costs or fixed costs

helpful to understand the relationship among variable costs, fixed costs
and profit
Assumptions of CVP Analysis
1. revenues change in relation to production and sales
2. costs can be divided in variable and fixed categories and fixed
element constant over the relevant range
3. revenues and costs behave in a linear fashion
4. costs and prices are known
5. if more than one product exists, the sales mix is constant
6.
inventories stay at the same level
7. we can ignore the time value of money
Fall 2010
EMBA 5403
6/109
Page 67
Contribution Margin
 Contribution margin is equal to the difference between
total revenue and total variable costs
Contribution margin per unit
= Selling price - Variable cost per unit
Contribution margin percentage
= Contribution margin per unit / selling price per unit
Per Unit
Revenue
Variable costs
Contribution margin
Fall 2010
EMBA 5403
$200
120
$80
Total for
2 units
$400
240
$160
%
100%
60%
40%
7/109
Pages 68 - 69
Contribution Margin Income
Statement
 Income statement that groups line items by cost
behaviour to highlight the contribution margin
0
Revenue
Packages Sold
1
2
25
40
$0
$200
$400$5,000 $8,000
Variable costs
0
120
240 3,000 4,800
Contribution margin
0
80
160 2,000 3,200
2,000
2,000
2,000 2,000 2,000
Fixed costs
Operating income$(2,000)$(1,920)$(1,840) $0 $1,200
Fall 2010
EMBA 5403
8/109
Page 69
Breakeven Point
 Quantity of output where total revenues equal total
costs
 Point where operating income equals zero
Breakeven point in units
= Fixed costs / Contribution margin per unit
= $2,000 / $80
= 25 units
Breakeven point in dollars
= Fixed costs / contribution margin %
= $2,000 / 40%
= $5,000
Fall 2010
EMBA 5403
9/109
Page 71
Cost-Volume-Profit Graph
$10,000
Total revenues
line
Breakeven
Point
25 units
$8,000
Total costs
line
$6,000
Operating
income
$4,000
$2,000
Operating
loss
$0
0
10
20
30
40
50
Units Sold
Fall 2010
EMBA 5403
10/109
Page 72
Target Operating Income
 For most firms in the private sector, the main
objective is not to breakeven
 Convert after-tax desired net income to its
before-tax equivalent operating income
Target operating income
= Target net income / (1 - tax rate)
Target Unit Sales
= (Fixed costs + Target operating income)
/ Contribution margin per unit
Target Dollar Sales
= (Fixed costs + Target operating income)
/ Contribution margin %
Fall 2010
EMBA 5403
11/109
Pages 73 - 75
Sensitivity Analysis
 sensitivity analysis is a “what-if” technique that
examines how a result will change if the original
predicted data are not achieved or if an underlying
assumption changes
 What will happen to operating income if volume
declines by 5%?
 What will happen to operating income if variable
costs increase by 10% per unit?
 sensitivity analysis broadens management’s
perspectives about possible outcomes
Fall 2010
EMBA 5403
12/109
Pages 76 - 77
Alternative Cost Structures
 CVP helps managers assess the risks and potential
benefits of adopting alternative cost structures
Example: Alternative rental arrangements
Option 2
$1,400 Fixed Fee
+ 5% Commission
Option 1
$2,000 Fixed Fee
Rev
$
Rev
$
Cost
Units
Breakeven = 25 units
Fall 2010
EMBA 5403
Option 3
20% Commission
Rev
$
Cost
Cost
Units
Units
Breakeven = 20 units
Breakeven = 0 units
13/109
Pages 77 - 78
Basics of Cost-Volume-Profit
Analysis
Fall 2010
EMBA 5403
CM is used first to cover fixed
expenses. Any remaining CM
contributes to net operating income.
14/109
The Contribution Approach
Sales, variable expenses, and contribution margin can
also be expressed on a per unit basis. If Racing sells
an additional bicycle, $200 additional CM will be
generated to cover fixed expenses and profit.
Fall 2010
EMBA 5403
15/109
The Contribution Approach
Each month Racing must generate at least
$80,000 in total CM to break even.
Fall 2010
EMBA 5403
16/109
The Contribution Approach
If Racing sells 400 units in a month, it will be
operating at the break-even point.
Fall 2010
EMBA 5403
17/109
The Contribution Approach
If Racing sells one more bike (401
bikes), net
operating income will increase by $200.
Fall 2010
EMBA 5403
18/109
The Contribution Approach
We do not need to prepare an income statement
to estimate profits at a particular sales volume.
Simply multiply the number of units sold above
break-even by the contribution margin per unit.
If Racing sells
430 bikes, its
net income will
be $6,000.
Fall 2010
EMBA 5403
19/109
CVP Relationships in Graphic Form
The relationship among revenue, cost, profit and
volume can be expressed graphically by
preparing a CVP graph. Racing developed
contribution margin income statements at 300,
400, and 500 units sold. We will use this
information to prepare the CVP graph.
Income
300 units
Sales
$ 150,000
Less: variable expenses
90,000
Contribution margin
$
60,000
Less: fixed expenses
80,000
Net operating income
$ (20,000)
Fall 2010
EMBA 5403
Income
400 units
$ 200,000
120,000
$ 80,000
80,000
$
-
Income
500 units
$ 250,000
150,000
$ 100,000
80,000
$ 20,000
20/109
CVP Graph
450.000
400.000
350.000
300.000
250.000
In a CVP graph, unit volume is
usually represented on the
horizontal (X) axis and dollars on
the vertical (Y) axis.
200.000
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
Fall 2010
EMBA 5403
21/109
CVP Graph
450.000
400.000
350.000
300.000
250.000
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
Fall 2010
EMBA 5403
22/109
CVP Graph
450.000
400.000
350.000
300.000
250.000
Total Expenses
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
Fall 2010
EMBA 5403
23/109
CVP Graph
450.000
400.000
Total Sales
350.000
300.000
250.000
Total Expenses
200.000
Fixed Expenses
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
Fall 2010
EMBA 5403
24/109
CVP Graph
450.000
Break-even point
(400 units or $200,000 in sales)
400.000
350.000
300.000
250.000
200.000
150.000
100.000
50.000
-
100
200
300
400
500
600
700
800
Units
Fall 2010
EMBA 5403
25/109
Contribution Margin Ratio
The contribution margin ratio is:
CM Ratio =
Total CM
Total sales
For Racing Bicycle Company the ratio is:
$80,000
= 40%
$200,000
Each $1.00 increase in sales results in a
total contribution margin increase of 40¢.
Fall 2010
EMBA 5403
26/109
Contribution Margin Ratio
Or, in terms of units, the contribution margin
ratio is:
CM Ratio =
Unit CM
Unit selling price
For Racing Bicycle Company the ratio is:
$200 = 40%
$500
Fall 2010
EMBA 5403
27/109
Contribution Margin Ratio
400 Bikes
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
-
500 Bikes
$ 250,000
150,000
100,000
80,000
$ 20,000
A $50,000 increase in sales revenue
results in a $20,000 increase in CM.
($50,000 × 40% = $20,000)
Fall 2010
EMBA 5403
28/109
CONTRIBUTION MARGIN RATIO
CMR= CONTRIBUTION MARGIN RATIO
= CM / SALES OR cmu/p
VCR = VARIABLE COST RATIO
= VC/SALES OR vcu/p
CMR +VCR= 1
EFFECT OF CHANGE IN FIXED COSTS?
EFFECT OF CHANGE IN VARIABLE COSTS?
EFFECT OF CHANGE IN SELLING PRICE?
Fall 2010
EMBA 5403
29/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average selling
price of a cup of coffee is $1.49 and the average
variable expense per cup is $0.36. The average
fixed expense per month is $1,300. 2,100 cups
are sold each month on average. What is the CM
Ratio for Coffee Klatch?
a. 1.319
b. 0.758
c. 0.242
d. 4.139
Fall 2010
EMBA 5403
30/109
Quick Check 
Coffee Klatch is an espresso stand in a downtown
office building. The average selling price of a cup of
coffee is $1.49 and the average variable expense per
cup is $0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month on
average. What is the CM Ratio for Coffee Klatch?
a. 1.319
b. 0.758
Unit contribution margin
CM Ratio =
Unit selling price
c. 0.242
d. 4.139
($1.49-$0.36)
=
=
Fall 2010
EMBA 5403
$1.49
$1.13
= 0.758
$1.49
31/109
Changes in Fixed Costs and Sales
Volume
What is the profit impact if Racing
can increase unit sales from 500
to 540 by increasing the monthly
advertising budget by $10,000?
Fall 2010
EMBA 5403
32/109
Changes in Fixed Costs and Sales
$80,000 + $10,000 advertising = $90,000
Volume
Sales increased by $20,000, but net operating
Fall 2010
33/109
income
decreased
by
$2,000.
EMBA 5403
Changes in Fixed Costs and Sales
Volume
The Shortcut Solution
Increase in CM (40 units X $200)
Increase in advertising expenses
Decrease in net operating income
Fall 2010
EMBA 5403
$ 8,000
10,000
$ (2,000)
34/109
Change in Variable Costs and Sales
Volume
What is the profit impact if Racing can
use higher quality raw materials, thus
increasing variable costs per unit by $10,
to generate an increase in unit sales
from 500 to 580?
Fall 2010
EMBA 5403
35/109
Change in Variable Costs and Sales
Volume
580 units × $310 variable cost/unit = $179,800
Sales increase by $40,000, and net operating income
Fall 2010
36/109
increases
by
$10,200.
EMBA 5403
Change in Fixed Cost, Sales Price and Volume
What is the profit impact if Racing (1) cuts its selling
price $20 per unit, (2) increases its advertising budget
by $15,000 per month, and (3) increases unit sales
from 500 to 650 units per month?
Fall 2010
EMBA 5403
37/109
Change in Fixed Cost, Sales Price and
Volume
Sales increase by $62,000, fixed costs increase by
$15,000,
and net operating income increases by $2,000.
Fall 2010
38/109
EMBA 5403
Change in Variable Cost, Fixed Cost and Sales Volume
What is the profit impact if Racing (1) pays a $15 sales
commission per bike sold instead of paying salespersons flat
salaries that currently total $6,000 per month, and (2) increases
unit sales from 500 to 575 bikes?
Fall 2010
EMBA 5403
39/109
Change in Variable Cost, Fixed Cost and Sales Volume
Sales increase by $37,500, variable costs increase by
$31,125, but fixed expenses decrease by $6,000.40/109
Fall 2010
EMBA 5403
Change in Regular Sales Price
If Racing has an opportunity to sell 150 bikes to a
wholesaler without disturbing sales to other customers
or fixed expenses, what price would it quote to the
wholesaler if it wants to increase monthly profits by
$3,000?
Fall 2010
EMBA 5403
41/109
Change in Regular Sales
Price
$ 3,000 ÷ 150 bikes =
Variable cost per bike =
Selling price required =
$ 20 per bike
300 per bike
$ 320 per bike
150 bikes × $320 per bike = $ 48,000
Total variable costs
=
45,000
Increase in net income
= $ 3,000
Fall 2010
EMBA 5403
42/109
Break-Even Analysis
Break-even analysis can be
approached in two ways:
1.Equation method
2.Contribution margin
method
Fall 2010
EMBA 5403
43/109
Equation Method
Profits = (Sales – Variable expenses) – Fixed expenses
OR
Sales = Variable expenses + Fixed expenses + Profits
At the break-even point
profits equal zero
Fall 2010
EMBA 5403
44/109
Break-Even Analysis
Here is the information from Racing Bicycle
Company:
Total
Sales (500 bikes)
$ 250,000
Less: variable expenses 150,000
Contribution margin
$ 100,000
Less: fixed expenses
80,000
Net operating income
$ 20,000
Fall 2010
EMBA 5403
Per Unit
$
500
300
$
200
Percent
100%
60%
40%
45/109
Equation Method
We calculate the break-even point as
follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
Where:
Q = Number of bikes sold
$500 = Unit selling price
$300 = Unit variable expense
$80,000 = Total fixed expense
Fall 2010
EMBA 5403
46/109
Equation Method
We calculate the break-even point as
follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
$200Q = $80,000
Q = $80,000 ÷ $200 per bike
Q = 400 bikes
Fall 2010
EMBA 5403
47/109
Equation Method
The equation can be modified to calculate the
break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
Where:
X = Total sales dollars
0.60 = Variable expenses as a % of sales
$80,000 = Total fixed expenses
Fall 2010
EMBA 5403
48/109
Equation Method
The equation can be modified to calculate
the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
0.40X = $80,000
X = $80,000 ÷ 0.40
X = $200,000
Fall 2010
EMBA 5403
49/109
Contribution Margin Method
The contribution margin method
has two key equations.
Break-even point
=
in units sold
Break-even point in
total sales dollars =
Fall 2010
EMBA 5403
Fixed expenses
Unit contribution margin
Fixed expenses
CM ratio
50/109
Contribution Margin Method
Let’s use the contribution margin method to
calculate the break-even point in total
sales dollars at Racing.
Break-even point in
total sales dollars =
Fixed expenses
CM ratio
$80,000
= $200,000 break-even sales
40%
Fall 2010
EMBA 5403
51/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per
month is $1,300. 2,100 cups are sold each
month on average. What is the break-even
sales in units?
a. 872 cups
b. 3,611 cups
c. 1,200 cups
d. 1,150 cups
Fall 2010
52/109
EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the break-even
sales in
Fixed expenses
Break-even
Unit CM
units?
= $1,300
a. 872 cups
= $1.49/cup - $0.36/cup
b. 3,611 cups
$1,300
= $1.13/cup
c. 1,200 cups
= 1,150 cups
d. 1,150 cups
Fall 2010
53/109
EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the break-even sales in
dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129
Fall 2010
54/109
EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the break-even sales in
dollars?
Fixed expenses
Break-even
=
a. $1,300
CM Ratio
sales
$1,300
b. $1,715
=
0.758
c. $1,788
= $1,715
d. $3,129
Fall 2010
55/109
EMBA 5403
DERIVATION OF EQUATIONS
SALES= VARIABLE COSTS+FIXED COSTS + PROFIT
p*q= vcu *q + FC + ¶
AT BREAKEVEN PROFIT = 0
p*q=vcu *q +FC
q * (p-vcu) = FC
q= FC / (p - vcu) OR q=FC/ cmu
CM= SALES - TOTAL VC
VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND
SELLING EXPENSES
cmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/q
vcu= VARIABLE COST PER UNIT= VC/ q
q number of units
Fall 2010
EMBA 5403
56/109
PROFIT ANALYSIS
 AT BREAKEVEN PROFIT = 0
 BEFORE BREAKEVEN LOSS; AFTER BREAKEVEN
PROFIT
 CM COVERS FIXED COST UPTO BREAKEVEN POINT
 AFTER BREAKEVEN POINT INCREASE IN CM WILL
INCREASE NET INCOME
 CM = FC + INCOME BEFORE TAX
Fall 2010
EMBA 5403
57/109
Target Profit Analysis
The equation and contribution margin
methods can be used to determine the
sales volume needed to achieve a target
profit.
Suppose Racing Bicycle Company
wants to know how many bikes
must be sold to earn a profit of
$100,000.
Fall 2010
EMBA 5403
58/109
The CVP Equation Method
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $100,000
$200Q = $180,000
Q = 900 bikes
Fall 2010
EMBA 5403
59/109
The Contribution Margin Approach
The contribution margin method can be used
to determine that 900 bikes must be sold to
earn the target profit of $100,000.
Unit sales to attain
=
the target profit
Fixed expenses + Target profit
Unit contribution margin
$80,000 + $100,000
= 900 bikes
$200/bike
Fall 2010
EMBA 5403
60/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. How many cups of coffee would
have to be sold to attain target profits of
$2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups
Fall 2010
61/109
EMBA 5403
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. How many cups of coffee would
have to be sold to attain target profits of
$2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups
Fall 2010
62/109
EMBA 5403
Unit breakeven
Unit sales
Fixed expenses + Target profit
to attain =
Unit CM
target profit
$1,300 + $2,500
=
$1.49 - $0.36
=
$3,800
$1.13
= 3,363 cups
Fall 2010
EMBA 5403
63/109
The Margin of Safety
The margin of safety is the excess of
budgeted (or actual) sales over the
break-even volume of sales.
Margin of safety = Total sales - Break-even sales
Let’s look at Racing Bicycle Company and
determine the margin of safety.
Fall 2010
EMBA 5403
64/109
The Margin of Safety
If we assume that Racing Bicycle Company has
actual sales of $250,000, given that we have
already determined the break-even sales to be
$200,000, the margin of safety is $50,000 as
shown
Break-even
sales
400 units
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
Fall 2010
EMBA 5403
Actual sales
500 units
$ 250,000
150,000
100,000
80,000
$
20,000
65/109
The Margin of Safety
The margin of safety can be
expressed as 20% of sales.
($50,000 ÷ $250,000)
Break-even
sales
400 units
Sales
$ 200,000
Less: variable expenses
120,000
Contribution margin
80,000
Less: fixed expenses
80,000
Net operating income
$
Fall 2010
EMBA 5403
Actual sales
500 units
$ 250,000
150,000
100,000
80,000
$
20,000
66/109
The Margin of Safety
The margin of safety can be expressed in
terms of the number of units sold. The
margin of safety at Racing is $50,000,
and each bike sells for $500.
Margin of
$50,000
=
= 100 bikes
Safety in units
$500
Fall 2010
EMBA 5403
67/109
MARGIN OF SAFETY
EXCESS OF SALES (EITHER ACTUAL OR FORECASTED ) OVER
THE BREAKEVEN SALES I.E., THE BUFFER AMOUNT
MoS $= ACTUAL OR BUDGETED SALES - BREAKEVEN SALES $
MoS % = MoS $ / ACTUAL OR BUDGETED SALES
BREAKEVEN SALES IN SINGLE PRODUCT SETTING
SALES $ = VC$ + FC$
WHERE VCR= x% *SALES THEN
1-x% = CMR
SALES $
= x% *SALES +FC
(1-x)* SALES $ = FC THAT IS CMR*SALES = FC
SALES $ AT BREAKEVEN = FC/ CMR
Fall 2010
EMBA 5403
68/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the margin of safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
Fall 2010
EMBA 5403
69/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the margin of safety?
a. 3,250 cups
b. 950 cups
c. 1,150 cups
d. 2,100 cups
Fall 2010
EMBA 5403
70/109
Margin of Safety
Margin of safety = Total sales – Break-even sales
= 2,100 cups – 1,150 cups
= 950 cups
or
950 cups
Margin of safety
= 2,100 cups = 45%
percentage
Fall 2010
EMBA 5403
71/109
Cost Structure and Profit
Stability
Cost structure refers to the relative proportion
of fixed and variable costs in an organization.
Managers often have some latitude in
determining their organization’s cost structure.
Fall 2010
EMBA 5403
72/109
Cost Structure and Profit
Stability
There are advantages and disadvantages to high
fixed cost (or low variable cost) and low fixed
cost (or high variable cost) structures.
An advantage of a high fixed
cost structure is that income
will be higher in good years
compared to companies
A disadvantage of a high fixed
with lower proportion of
cost structure is that income
fixed costs.
will be lower in bad years
compared to companies
with lower proportion of
Fall 2010
73/109
fixed
costs.
EMBA 5403
Operating Leverage
 A measure of how sensitive net operating
income is to percentage changes in sales.
Degree of
Contribution margin
=
operating leverage
Net operating income
Fall 2010
EMBA 5403
74/109
Operating Leverage
At Racing, the degree of operating leverage is 5.
Actual sales
500 Bikes
Sales
$ 250,000
Less: variable expenses
150,000
Contribution margin
100,000
Less: fixed expenses
80,000
Net income
$ 20,000
Fall 2010
EMBA 5403
$100,000
= 5
$20,000
75/109
Operating Leverage
With an operating leverage of 5, if Racing
increases its sales by 10%, net operating
income would increase by 50%.
Percent increase in sales
Degree of operating leverage
Percent increase in profits
×
10%
5
50%
Here’s the verification!
Fall 2010
EMBA 5403
76/109
Operating Leverage
Actual sales
(500)
Sales
$ 250,000
Less variable expenses
150,000
Contribution margin
100,000
Less fixed expenses
80,000
Net operating income
$
20,000
Increased
sales (550)
$ 275,000
165,000
110,000
80,000
$
30,000
10% increase in sales from
$250,000 to $275,000 . . .
Fall 2010
EMBA 5403
. . . results in a 50% increase in
77/109
income from $20,000 to $30,000.
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92
Fall 2010
EMBA 5403
78/109
Quick Check 
Coffee Klatch is an espresso stand in a
downtown office building. The average
selling price of a cup of coffee is $1.49 and
the average variable expense per cup is
$0.36. The average fixed expense per month
is $1,300. 2,100 cups are sold each month
on average. What is the operating leverage?
a. 2.21
b. 0.45
Operating Contribution margin
c. 0.34
leverage = Net operating income
d. 2.92
$2,373
= $1,073 = 2.21
Fall 2010
EMBA 5403
79/109
Con’t
Actual sales
2,100 cups
Sales
$
3,129
Less: Variable expenses
756
Contribution margin
2,373
Less: Fixed expenses
1,300
Net operating income
$
1,073
Fall 2010
EMBA 5403
80/109
Quick Check 
At Coffee Klatch the average selling price of a cup
of coffee is $1.49, the average variable expense per
cup is $0.36, and the average fixed expense per
month is $1,300. 2,100 cups are sold each month on
average.
If sales increase by 20%, by how much should net
operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%
Fall 2010
EMBA 5403
81/109
Quick Check 
At Coffee Klatch the average selling price of
a cup of coffee is $1.49, the average variable
expense per cup is $0.36, and the average
fixed expense per month is $1,300. 2,100 cups
are sold each month on average.
If sales increase by 20%, by how much
should net operating income increase?
a. 30.0%
Percent increase in sales
20.0%
b. 20.0%
× Degree of operating leverage
2.21
c. 22.1%
Percent increase in profit
44.20%
d. 44.2%
Fall 2010
EMBA 5403
82/109
Cost Structure and Operating
Leverage
Operating leverage is greatest in companies that
have a high proportion of fixed costs in relation
to variable costs.
Sales
Variable Expense
CM
Fixed Expenses
Net Income
Operating Leverage Factor
Fall 2010
EMBA 5403
Company A
$
500.000
300.000
200.000
150.000
$
50.000
Company B
$ 500.000
50.000
450.000
400.000
$
50.000
200.000
50.000
4
450.000
50.000
9
83/109
Operating Leverage Factor
 A measure of how a percentage
change in sales will affect profits.
Operating leverage
factor
=
Contribution margin
Net income
 The greater the operating
leverage, the greater the
sensitivity of its profit to changes
in volume.
Fall 2010
EMBA 5403
84/109
Operating Leverage Factor
If Company A and B increases
its sales by 10%, which
company will have the
greatest change in net income
and why?
Fall 2010
EMBA 5403
85/109
COST STRUCTURE AND PROFITABILITY






HIGH VARIABLE COSTS LEAD TO LOWER CM AND LESS
VULNERABLE IN CRISIS TIME
HIGH FIXED COSTS CAUSE HIGHER BREAKEVEN POINT;
AFTER THE BREAKEVEN POINT PROFITS INCREASE
FASTER THAN THE HIGH VARIABLE COST COMPANY
DEGREE OF OPERATING LEVERAGE: CONTRIBUTION
MARGIN / NET INCOME
FOR A GIVEN % CHANGE IN SALES, INCOME WILL
INCREASE BY (% INCREASE IN SALES *DEGREE OF
OPERATING LEVERAGE)
DEGREE OF OPERATING LEVERAGE DECREASES AS THE
SALES MOVE AWAY FROM THE BREAKEVEN POINT
IF VARIABLE COSTS ARE HIGH DEGREE OF OPERATING
LEVERAGE LOW; AND VICE VERSA
Fall 2010
EMBA 5403
86/109
Verify Increase in Profit
Actual
sales
2,100 cups
Sales
$ 3,129
Less: Variable expenses
756
Contribution margin
2,373
Less: Fixed expenses
1,300
Net operating income
$ 1,073
% change in sales
% change in net operating income
Fall 2010
EMBA 5403
Increased
sales
2,520 cups
$
3,755
907
2,848
1,300
$
1,548
20.0%
44.2%
87/109
Structuring Sales Commissions
Companies generally compensate
salespeople by paying them either a
commission based on sales or a salary plus a
sales commission. Commissions based on
sales dollars can lead to lower profits in a
company.
Let’s look at an example.
Fall 2010
EMBA 5403
88/109
Structuring Sales Commissions
Pipeline Unlimited produces two types of surfboards,
the XR7 and the Turbo. The XR7 sells for $100 and
generates a contribution margin per unit of $25. The
Turbo sells for $150 and earns a contribution margin
per unit of $18.
The sales force at Pipeline Unlimited is
compensated based on sales commissions.
Fall 2010
EMBA 5403
89/109
Structuring Sales Commissions
If you were on the sales force at Pipeline, you would
push hard to sell the Turbo even though the XR7
earns a higher contribution margin per unit.
To eliminate this type of conflict, commissions can
be based on contribution margin rather than on
selling price alone.
Fall 2010
EMBA 5403
90/109
The Concept of Sales Mix
 Sales mix is the relative proportion in
which a company’s products are sold.
 Different products have different selling
prices, cost structures, and contribution
margins.
Let’s assume Racing Bicycle Company sells
bikes and carts and that the sales mix
between the two products remains the
same.
Fall 2010
EMBA 5403
91/109
Revenue Mix
Revenue mix (or sales mix) is the
relative combination of quantities of
products or services that make up
total revenue
Fall 2010
EMBA 5403
92/109
Pages 73 - 75
Multi-product break-even analysis
Racing Bicycle Co. provides the following information:
Fall 2010
EMBA 5403
$265,000
93/109
= 48.2% (rounded)
$550,000
Multi-product break-even
Break-even
Fixed expenses
=
analysis
sales
CM Ratio
$170,000
=
48.2%
= $352,697
Fall 2010
EMBA 5403
94/109
SALES MIX= % OF TOTAL SALES FOR EVERY PRODUCT
THREE PRODUCTS A , B, C
% SALES OF a, b , c where a= sales of product a / total sales etc.
CMa = CM OF PRODUCT A, B OR C
WEIGHTED CMR= a * CMR of product A + b * CMR of product B + c *
CMR of product C
BREAKEVEN IN MULTIPLE PRODUCT S= FC/ WEIGHTED CMR
•TO FIND HOW MANY UNITS MUST BE SOLD AT BREAKEVEN (OR
FOR TARGET INCOME):
1.FIND BREAKEVEN IN MULTIPLE PRODUCTS
2.COMPUTE EACH PRODUCTS SALES AMOUNT BY MULTIPLYING
THE SALES RATIO * BREAKEVEN SALES
3.FIND THE BREAKEVEN SALE SHARE OF EACH PRODUCT;
4.DIVIDE EACH PRODUCTS SHARE OF BREAKEVEN SALES BY
THE UNIT PRICE OF EACH PRODUCT TO GET THE NUMBER OF
UNITS TO BE SOLD OF EACH PRODUCT IN ORDER TO BREAKEVEN
OR FOR TARGET INCOME
Fall 2010
EMBA 5403
95/109
Key Assumptions of CVP
Analysis
 Selling price is constant.
 Costs are linear.
 In multi-product companies, the
sales mix is constant.
 In manufacturing companies,
inventories do not change (units
produced = units sold).
Fall 2010
EMBA 5403
96/109
Multiple Cost Drivers
 In many cases there may be multiple cost drivers
Do-All Software Example
Variable costs:
$40 per software package sold
$15 per invoice issued
Operating income
= Revenue – ($40 x packages sold) – ($15 x invoices
issued) – Fixed costs
 In cases where there are multiple cost drivers there
are multiple breakeven points
Fall 2010
EMBA 5403
97/109
Examples
 Please do the exercises before the
next session.
Fall 2010
EMBA 5403
98/109
Contribution Margin & Gross Margin
Merchandising Sector
Gross Margin
Format
Contribution Margin
Format
Revenues
Variable costs:
Cost of goods sold
Other variable
Contribution margin
Fixed costs:
Cost of goods sold
$200
$120
43
5
163
37
Other fixed
19 24
Operating income $13
Fall 2010
EMBA 5403
Revenues
$200
Cost of goods sold (120+5)
125
Gross margin
75
Operating costs (43+19)
62
Operating income
$13
99/109
Pages 82 - 83
Example 1: equation approach
•
•
•
•
•
Movie theater: $48,000 monthly fixed costs
$8 ticket price.
$2 variable cost per ticket.
$6 contribution margin per ticket; 75% cont. margin ratio
Give breakeven units and revenue
BEunits = $48,000/($8 - $2)
BEunits = 8,000 tickets.
BErevenue = $64,000
Fall 2010
EMBA 5403
100/109
$000
(per month)
40
30
Profit
20
Break-even point: 8,000 tickets
10
Profit
area
0
-10
-20
Loss
2,000
4,000
6,000
Loss area
-30
8,000
10,000
Volume of
tickets sold
in one
month
-40
-50
Fall 2010
EMBA 5403
Fixed expenses = $48,000
101/109
Example 1 Cont’d
• Suppose practical capacity per month is 12,000
tickets and that the movie theater has operated
at 60% capacity during December. It is now
December 30.
• Has the theater made money in December?
• If they could capture 1,000 customers by
lowering the ticket price to $7 for New Year’s
Eve, should they do it?
Fall 2010
EMBA 5403
102/109
Example 1 con’t
practical capacity
operating at
contribution
fixed costs
loss
12000 tickets
60%
=60% *12000*6=
43200
48000
-4800
7-2
add'l contribution
Fall 2010
EMBA 5403
1000
5
5000 >
200 net income
yes, they should
4800
103/109
Example 2
Data: The Doral Company manufactures and
sells pens. Present sales output is 5,000,000
per year at a selling price of $.50 per unit.
Fixed costs are $900,000 per year. Variable
costs are $.30 per unit.
 What is the current yearly operating income?
 What is the current breakeven point in sales
dollars?
Fall 2010
EMBA 5403
104/109
Example 2 Cont’d –answer part 1
Contribution margin ratio =
total contribution margin =
Fixed Cost
operating income
Breakeven Sales =
Fall 2010
EMBA 5403
$.20/$.50=
$1,000,000
$900,000
$100,000
40%
900,000/60%=
$2,250,000
105/109
Example 2 Cont’d – question part 2
Compute the new operating income if . . .
1. A $.04 per-unit increase in variable
costs.
2. A 20% decrease in fixed costs, a 20%
decrease in selling price, a 10%
decrease in variable costs, and a 40%
increase in units sold.
Fall 2010
EMBA 5403
106/109
Example 2 Cont’d –answer part 2
1. $0.04 increase in variable costs
new variable cost
0.34
new cont. margin per pen
0.16
total sales
5,000,000 pens
total cont. margin =
$800,000
Fixed costs
$900,000
operating income
($100,000)
2. A 20% decrease in fixed costs, a 20% decrease in
selling price, a 10% decrease in variable costs, and a
40% increase in units sold.
new selling price
new variable costs
new units sold
total cont. margin =
Fixed costs
operating income
Fall 2010
EMBA 5403
$0.40
$0.27
7,000,000 pens
$1,890,000
$900,000
$990,000
107/109
Example 2 Cont’d-questions part 3
Compute the new breakeven point in units
for
each of the following changes.
 A 10% increase in fixed costs:
 A 10% increase in selling price and a
$20,000 increase in fixed costs.
Fall 2010
EMBA 5403
108/109
Example 2 Cont’d –answer part 3
new BE units if fixed cost increase by 10%
new fixed costs
contribution margin per pen
New BE units
$990,000
$0.20
4,950,000 pens
new BE units if selling price increase by 10%
and fixed cost increase by $20.000.
$0.55 per pen
new selling price
$920,000
new fixed costs
$0.25 per pen
new contribution margin
3,680,000 pens
New BE units
Fall 2010
EMBA 5403
109/109
Example 3
The Rapid Meal has two restaurants that are open 24
hours per day. Fixed costs for the two restaurants together
total $450,000 per year. Service varies from a cup of
coffee to full meals. The average sales check for each
customer is $8.00. The average cost of food and other
variable costs for each customer is $3.20. The income tax
rate is 30%. Target net income is $105,000.
Fall 2010
EMBA 5403
110/109
Example 3 Cont’d
Compute the total dollar sales needed
to obtain the target net income.
How many sales checks are needed to
break even?
Compute net income if the number of
sales checks is 150,000
Fall 2010
EMBA 5403
111/109
Example 3 - answers
Compute the total dollar sales needed to obtain the target net income
before tax income= 105000/0.7= $150,000
approach 1;
sales = vc +fc+before tax profit
sales = average sales check x no of customers
variable cost= vc per cust x no of customers
average check per customer =
8
variable cost per customer =
3.2
approach 2:
contribution margin per customer =
4.8
contribution margin ratio =
0.6
fixed costs =
$450,000
fixed cost + target income =
$600,000
Sales to reach target income =
$1,000,000 (600.000 /0.60)
Fall 2010
EMBA 5403
112/109
Example 3 - answers
How many sales checks are needed to break even?
fixed cost + target income =
contribution margin per customer =
number check (customers) to reach target income
$600,000
$4.80
125000
Compute net income if the number of sales checks is 150,000
contribution margin per customer =
number of sales checks (customers)=
total contribution margin
fixed costs =
income before tax
income tax
net income
Fall 2010
EMBA 5403
$4.80
150000
$720,000
$450,000
$270,000
81000
$189,000
113/109
Multiple-Product Example
Assume the following:
Units sold
Sales price per unit
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net income
Regular
Deluxe
Total
Percent
400
$
500
$200,000
120,000
$ 80,000
200
$750
$150,000
60,000
$ 90,000
600
---$350,000
180,000
$170,000
130,000
$ 40,000
=======
------100.0%
51.4
48.6%
1. What is the break even point?
2. How much sales revenue of each product must be generated to earn
a before tax profit $50,000?
Fall 2010
EMBA 5403
114/109
Multi product example -answer
1. What is the break even point?
fixed costs
weighted cont. margin ratio
BE sales dollars
$130,000
48.60%
$267,490
2. How much sales revenue of each product must be generated to earn
a before tax profit $50,000?
target income
fixed costs
weighted cont. margin ratio
fixed cost + target income
sales revenue targeted- total
sales mix (percent)
regular (200.000/350.000)
deluxe (150.000 / 350.000)
Sales of regular
Sales of deluxe
(sales mix % x sales target)
Fall 2010
EMBA 5403
$50,000
$130,000
48.60%
$180,000
$370,370.37
57.14%
42.86%
$211,640.21
$158,730.16
115/109
Multiple product - verify
cmr - regular
cmr - deluxe
contribution margin -regular
contribution margin - deluxe
total contribution
Fixed costs
before tax income
Fall 2010
EMBA 5403
40.00%
60.00%
$84,656.08
$95,238.10
$179,894.18
$130,000
$49,894.18
116/109
Example 4
 A financial analyst is studying the feasibility of two
alternative assembly methods, manual and
automated. The automated method has variable
costs of TL 2.10 per unit and annual committed
costs of TL 130.000; in contrast, the manual
method has variable costs of TL 4.20 per unit and
committed costs of TL 60.000. The company sells
its products for TL 23 per unit.
 What is break-even of each method?
 Above what volume level will management prefer
the automated method to the manual method?
Fall 2010
EMBA 5403
117/109
Selling price
Automated
variable
fixed
Example
4 Answer
Manual
variable
fixed
TL23.00
TL2.10 per unit
TL130,000 per year
TL4.20 per unit
TL60,000 per year
Automated BE units:
fixed cost
TL130,000
cont.per unit
TL20.90
BE units
6,220.10
6221 units
Manual BE units:
fixed cost
TL60,000
cont.per unit
TL18.80
BE units
Fall 2010
EMBA 5403
3,191.49
3.192 units
118/109
Example 4 answer
Find the indifference point:
2.1q+130000=4.2q+60000
change in cost
TL70,000
change in q
2.1
33333.333 33.334 units
after 33.334 units automated is better
at 35.000 units
at 30.000 units
manual
cont. margin per unit
number of units
Contribution Margin
Fixed Costs
Operating Income
Fall 2010
EMBA 5403
automated
TL18.80
TL20.90
35000
35000
TL658,000.00 TL731,500.00
manual
cont. margin per unit
number of units
Contribution Margin
TL60,000
TL130,000
Fixed Costs
TL598,000
TL601,500
Operating Income
automated
TL18.80
TL20.90
30000
30000
TL564,000.00 TL627,000.00
TL60,000
TL130,000
TL504,000
TL497,000
119/109